Name: _______________________________
The Summer Intro Packet is designed for students to review material from their previous mathematics course so they are ready to begin the 8 th
grade Introduction to
Algebra & Geometry course in the Fall. The expectation is that the concepts contained in the packet are mastered before beginning the Intro course in August.
This packet is to be completed by the first day of school.
-Show All Work! – enough space has been provided on the packet itself, however, if you do not feel you have enough space to show your work on a given problem, please show your work on a separate sheet of paper. Staple any of your extra work to the packet.
-once finished, grade your packet and mark the appropriate box. Corrections should be done in a separate color to show difference
-if you need help with a concept, use the phschool.com
website to
watch the tutorials or practice examples
-any of the topics can also be Googled and many tutorials are
available online
- a quiz will be given on this material the first week of school
Be prepared to be successful in 8 th
grade math by completing your packet this summer, and making sure you understand all of the concepts within the packet by the first day of class in August.
Good Luck!

Name-Period: ________________________________
Introduction to Algebra & Geometry Summer Packet
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Identify the expression as a numerical expression or a variable expression . For a variable expression, name the variable.
____ 1.

7 a. numerical expression b. variable expression; d is the variable. c. variable expression; g is the variable. d. variable expression; there is no variable.
____ 2.

9 a. variable expression; i is the variable. b. variable expression; b is the variable. c. numerical expression d. variable expression; there is no variable.
____ 3. Write a variable expression for a number x divided by 5. a. x

6 b. 5 – x c. 5
 x d. x

5
____ 4. Write a word phrase that can be represented by k – 11. a. 11 more than a number k c. the difference of 11 and k b. 11 less than a number k d. the quotient of a number k and 11
Compare. Use >, <, or = to complete the statement.
____ 5. 6

–8
 c. < a. >
____ 6.
 –12  –11 b. = a. < b. >
Name the property shown.
____ 7. 4

0 = 4 a. Identity Property of Addition b. Commutative Property of Addition c. Commutative Property of Multiplication d. Associative Property of Addition c. =

Name the property shown.
____ 8. (9

2)

12 = 9

(2

12) a. Identity Property of Multiplication b. Associative Property of Multiplication c. Commutative Property of Multiplication d. Commutative Property of Addition
____ 9. (6

3)

12 = (3

6

12 a. Commutative Property of Addition b. Associative Property of Addition c. Commutative Property of Multiplication d. Identity Property of Addition
State whether the number is prime, composite, or neither.
____ 10. 19 a. neither b. prime
____ 11. 21 a. composite b. neither
____ 12. 1 a. prime b. composite
____ 13. Which fraction is equivalent to ? a. b. c.
____ 14. Which fraction is not equivalent to ? a. b. c.
Short Answer c. composite c. prime c. neither d. d.

Simplify. SHOW ALL WORK BELOW OR ON A SEPARATE SHEET OF PAPER.
17. 9 ∙ (5 + 5) + 3 18.
Evaluate. SHOW ALL WORK BELOW OR ON A SEPARATE SHEET OF PAPER.
19. 11 p

6, for p = 5 20.
21. 62

3 a , for a = 12
Simplify the expression. SHOW ALL WORK BELOW OR ON A SEPARATE SHEET OF PAPER.
22. 7 d – 8 + 4 d + 4 23. 2 v – 5 + 5 v
Use the Distributive Property to multiply. SHOW ALL WORK BELOW OR ON A SEPARATE
SHEET OF PAPER.
24. 4( b + 1) 25. –2(2 q – 1)
26. 27.

Show how to use mental math to simplify the expression. Think about the properties as shown in #7-9.
28. (17 + 15) + 83 29. 5

9

2 30. 55 + 29 – 15
Write an integer for each situation.
31. $19 lost 32. 8 steps forward 33. 6 floors up
34. During the day the temperature was . At night, the temperature dropped . What was the temperature at night?
38.
40.
35. The highest location in a certain country is 14,864 feet above sea level. The lowest point in the same country is 141 feet below sea level. a. Find the difference of the two elevations. b. A city is 7,642 feet above sea level. Is this elevation closer to the highest point or the lowest point?
Add or subtract. SHOW ALL WORK BELOW OR ON A SEPARATE SHEET OF PAPER.
36. 3.71 + 3.7
37. 7.3 – 1.77
39.
41.

42.
Divide or multiply. SHOW ALL WORK BELOW OR ON A SEPARATE SHEET OF PAPER.
43. 4
1

3
4
4
5
44.
45. Sue needs cups of flour for a batch of cookies. How many batches can she make with 9 cups of flour?
Solve each equation. SHOW ALL WORK BELOW OR ON A SEPARATE SHEET OF PAPER and
CHECK ALL SOLUTIONS!
46. p + 7 = 15
Check:
Check:
47. j – 5 = –8
Check:
48. 12 d = –72
Check:
49.
Check:
50. 5 x – 5 = 5
Check:
51. – 9 = –2

52.
53.
54.
55.
56. What is the prime factorization of 180? SHOW ALL WORK BELOW OR ON A SEPARATE SHEET
OF PAPER.
Find the GCF. SHOW ALL WORK BELOW OR ON A SEPARATE SHEET OF PAPER.
57. 40 and 45
58. Write in simplest form. SHOW ALL WORK.

59. A seventh-grade class has reached
15
17
7
8 its quota. If both classes have the same quota, which class is closer to reaching its quota?
60. You collect baseball cards. You have 16 out of 34 cards for a particular series (A) and 17 out of 37 cards for another series (B). For which series, A or B, do you have the greater fraction of cards?
Write the ratio as a fraction in simplest form. SHOW ALL WORK.
61. 18 to 2
62. In the population of a particular country, the male-to-female ratio is 46 to 54. Write this ratio as a fraction in simplest form. SHOW ALL WORK.
63. Find the cost of 10 notebooks if 3 notebooks cost $1.98. SHOW ALL WORK.
Write and solve an equation.
64. You withdrew $100 from the ATM machine. The new balance is $372. What was the original balance b of your account?
65. Alexa scored 87 on her history test. The test had a multiple-choice section and a short-answer section. Alexa got 74 points on the multiple-choice section. How many points p did she receive on the short-answer section?
66. Mark wants to buy a skateboard that costs $65. He plans to save $5 per week. How many weeks w will it take him to save $65?

67. This year, 14,265 people applied to a particular college. The number of applicants increased by 868 from last year. How many people p applied last year?
68. A baseball bat and 8 baseballs cost $163.25. The bat costs $106.45. What is the cost c of one baseball?
69. Raymond buys bottles of water at $2.10 each and a large pizza at $12.99. The total cost was $21.39. How many bottles of water b did he buy?
Solve the proportion. SHOW ALL WORK BELOW OR ON A SEPARATE SHEET OF PAPER and
CHECK ALL SOLUTIONS!!
Check:
70.
Check:
71.

8 th
Grade Introduction to Algebra and Geometry
Answer Key
Check your answers after completing each section. Check whichever statement applies to you.
Page 2
Answer
I got it on the 1 st try!
I got it with corrections.
I have no idea.
1 a
2 b
3 d
4 b
5 c
6 b
7 a
8 b
9 a
10 b
11 a
12 c
13 a
14 c
15 -43
16 -19
17 93
18 24
19 49
20 44
21 98
22 11 d – 4
23 7 v – 5
24 4 b + 4
25 -4 q + 2
26 6 x + 50
27 -7 c – 76
28 115
29 90
30 69
31 -19
32 8
33 6
34 -16° F
35 a) 15,005 ft; b) closer to highest point
36 7.41
37 5.53
38 25
33
39 3
9
4

40 8
8
9
41
42
43
5
36
1
8
4
20
5
44 3
4
45 3 full batches
46 p = 8
47 j = -3
48 d = -6
49 n = 77
50 x = 2
51 x = 14
52 x = -4
53 p = -3
54 w = 28
55 d = -9
56 2
2
· 3
2
· 5
57 5
58 8
11
59 7 th grade class
60 Series A
61 9
62 23
37
63 $6.60
64 $472
65 13 points
66 13 weeks
67 13,397 people
68 $7.10
69 4 bottles
70 x = 20
71 a = 20